Quantifying and mitigating the bullwhip effect in a benchmark supply chain system by an extended prediction self-adaptive control ordering policy

An undesired observation known as the bullwhip effect in supply chain management leads to excessive oscillations of the inventory and order levels. This paper presents how to quantify and mitigate the bullwhip effect by introducing model predictive control (MPC) strategy into the ordering policy for a benchmark supply chain system. Instead of quantifying the bullwhip effect with commonly used statistical measure, we derive equivalently the expression of bullwhip metric via control-theoretic approach by applying discrete Fourier transform and (inverse) z-transform when the demand signal is stationary stochastic. A four-echelon supply chain is formulated and its dynamical features are analyzed to give the discrete model. An extended prediction self-adaptive control (EPSAC) approach to the multi-step predictor is implemented in the development of MPC formulation. The closed-form solution to MPC problem is derived by minimizing a specified objective function. The transfer function for MPC ordering policy is then obtained graphically from an equivalent representation of this closed-form solution. A numerical simulation shows that MPC ordering policy outperforms the traditional ordering policies on reducing bullwhip effect.     

The governing dynamics of supply chains: The impact of altruistic behaviour

This paper analyses an infinite horizon two-echelon supply chain inventory problem and shows that a sequence of the optimum ordering policies does not yield globally optimal solutions for the overall supply chain. First-order autoregressive demand pattern is assumed and each participant adopts the order-up-to (OUT) policy with a minimum mean square error forecasting scheme to generate replenishment orders. To control the dynamics of the supply chain, a proportional controller is incorporated into the OUT policy, which we call a generalised OUT policy. A two-echelon supply chain with this generalised OUT policy achieves over 10% inventory related cost reduction. To enjoy this cost saving, the attitude of first echelon player to cost increases is an essential factor. This attitude also reduces the bullwhip effect. An important insight revealed herein is that a significant amount of benefit comes from the player doing what is the best for the overall supply chain, rather than what is the best for local cost minimisation.     

低碳环境下双渠道供应链线上线下广告策略的微分博弈分析

以一个由绿色制造商与零售商组成的双渠道供应链为研究对象,基于微分博弈分别比较分析集中式决策、采用竞争型广告策略的分散式决策与采用支持型广告策略的分散式决策模型下,双渠道供应链的最优均衡决策与最优利润.研究发现:集中式决策下的最优低碳水平、最优线上与线下广告水平均高于分散式决策,而产品最优销售价格可能高于、等于或低于分散式决策;分散式决策下,采用支持型广告策略的双渠道供应链的产品最优低碳水平、最优销售价格和最优线上广告投入水平与采用竞争型广告策略的双渠道供应链均衡策略一致;一定条件下,支持型广告策略使得分散式双渠道供应链得到Pareto改进,此时的最优线下广告投入水平优于竞争型广告策略下的最优线下广告投入水平.     

Fuzzy knowledge-based token-ordering policies for bullwhip effect management in supply chains

The “Bullwhip Effect” is a well-known example of supply chain inefficiencies and refers to demand amplification as moving up toward upstream echelons in a supply chain. This paper concentrates on representing a robust token-based ordering policy to facilitate information sharing in supply chains in order to manage the bullwhip effect. Takagi–Sugeno–Kang and hybrid multiple-input single-output fuzzy models are proposed to model the mechanism of token ordering in the token-based ordering policy. The main advantage of proposed fuzzy models is that they eliminate the exogenous and constant variables from the procedure of obtaining the optimal amount of tokens which should be ordered in every period. These fuzzy approaches model the mentioned mechanism through a push–pull policy. A four-echelon SC with fuzzy lead time and unlimited production capacity and inventory is considered to survey the outcomes. Numerical experiments confirm the effectiveness of proposed policies in alleviating BWE, inventory costs and variations.     

The impact of information sharing on ordering policies to improve supply chain performances

Bullwhip effect represents the amplification and distortion of demand variability as moving upstream in a supply chain, causing excessive inventories, insufficient capacities and high operational costs. A growing body of literature recognizes ordering policies and the lack of coordination as two main causes of the bullwhip effect, suggesting different techniques of intervention. This paper investigates the impact of information sharing on ordering policies through a comparison between a traditional (R, S) policy and a coordination mechanism based on ordering policy (a combination of (R, D) and (R, S) policies). This policy relies on a slow, easy to implement, information sharing to overcome drawbacks of the effect, in which replenishment orders are divided into two parts; the first is to inform the upstream echelons about the actual customer demand and the second is to inform about the adjustment of the inventory position, smoothing at the same time the orders of the different levels of the supply chain. A simulation model for a multi-echelon supply chain quantifies the supply chain dynamics under these different policies, identifying how information sharing succeeds to achieve an acceptable performance in terms of both bullwhip effect and inventory variance.     

含时滞的不确定性供应链网络系统牛鞭效应控制策略及其经济性能分析

考虑需求、生产能力、供应链结构等内外不确定性因素和供应链系统运作延迟,构建了不确定环境下含时滞的供应链库存网络系统状态转移模型.针对牛鞭效应问题,提出了基于库存水平波动状态的控制策略和相应的经济性能指标;借助线性矩阵不等式方法,深入分析库存策略的参数优化设计对牛鞭效应以及经济性能的影响.仿真结果表明,在经济性能约束下,该库存策略具有较强的牛鞭效应遏制能力,从而表明了策略的有效性和实用性.     

Adaptive logistic controller for integrated design of distributed supply chains

Usually each manufacturing stage in a supply chain makes its own decision regarding quantity and timing of parts it purchases from its suppliers, thereby controlling its inventory position and overall supply chain dynamics. Such decisions, although good for each individual stage, can adversely affect the overall performance of the supply chain. This can be viewed as distributed control of inventory, in which each controller is making autonomous decisions based on local objectives. Because these controllers do not have information about inventory position or order quantities at other stages, the safety stock tends to be higher, leading to higher inventories and cost. This also causes demand amplification and the bullwhip effect. This paper presents a distributed feedback control algorithm, called the Adaptive Logistics Controller (ALC), which simultaneously decides the order quantities for each stage of the supply chain to minimize the total WIP in the entire supply chain for a given demand. In this approach, simulation is used to provide the feedback to the ALC controller, leading to an iterative numerical computational approach. Computational experiments compared with the traditional centralized (Q,r)$(Q,r)$ policy model show that the order quantities calculated by the distributed ALC are much superior in terms of total overall WIP and hence result in lesser total costs for the entire supply chain.     

供应商管理库存对牛鞭效应的影响

采用基于z变换的离散传递函数和测量牛鞭效应的控制工程方法,计算了一个由一个供应商和一个用户组成的、使用指数平滑预测的供应商管理库存供应链和传统供应链的牛鞭效应,并比较了这两种供应链对牛鞭效应的影响.通过仿真证实,应用供应商管理库存策略对供应链的物理过程进行再造是一种有效的减少牛鞭效应的方法.     

Controller design and reduction of bullwhip for a model supply chain system using z-transform analysis

In this work, a discrete time series model of a supply chain system is derived using material balances and information flow. Transfer functions for each unit in the supply chain are obtained by z-transform. The entire chain can be modeled by combining these transfer functions into a close loop transfer function for the network. The model proves to be very useful in revealing the dynamics characteristic of the system. The system can be viewed as a linear discrete system with lead time and operating constraints. The stability of the system can be analyzed using the characteristic equation. Controllers are designed using frequency analysis. The bullwhip effect, i.e. magnification of amplitudes of demand perturbations from the tail to upstream levels of the supply chain, is a very important phenomenon for supply chain systems. We proved that intuitive operation of a supply chain system with demand forecasting will cause bullwhip. Moreover, lead time alone would not cause bullwhip. It does so only when accompanied by demand forecasting. Furthermore, we show that by implementing a proportional intergral or a cascade inventory position control and properly synthesizing the controller parameters, we can effectively suppress the bullwhip effect. Moreover, the cascade control structure is superior in meeting customer demand due to its better tracking of long term trends of customer demand.     

The benefit of VMI strategies in a stochastic multi-product serial two echelon system

We consider a multi-product serial two echelon inventory system with stochastic demand. Inventories at the downstream location are replenished periodically using an automatic ordering system. Under vendor managed inventory strategies the upstream stage is allowed to adapt these orders in order to benefit from economies of scale. We propose three different VMI strategies, aiming to reduce the order picking cost at the upstream location and the transportation costs resulting in reduced total supply chain costs. In a detailed numerical study the VMI strategies are compared with a retailer managed inventory strategy for two different demand models suitable for slow moving products. It is shown that if inventory holding costs are low, compared to handling and transportation costs, efficiencies at the warehouse are improved and total supply chain costs are reduced.     

Bullwhip effect measure in a seasonal supply chain

In this study, the bullwhip effect in a seasonal supply chain was quantified by considering a two echelon supply chain which consists of one supplier and one retailer. The external demand occurring at the customer was assumed to follow a SARMA (1, 0) X (0, 1) _s scheme, a seasonal autoregressive-moving average process, while the retailer employed an base-stock policy to replenish their inventory. The demand forecast was performed with a SARMA (1, 0) X (0, 1) _s using the minimum mean-square error forecasting technique. In order to develop the bullwhip effect measure in a seasonal supply chain, the lead time demand forecast, forecast error, and the optimal inventory policy at the retailer were derived in sequence. The variance of order quantity based on these results was obtained. Then, various properties were derived by analyzing the bullwhip effect measure. Specifically, it was determined that the seasonal cycle plays an important role in bullwhip effect under a seasonal supply chain. The findings also point out that the replenishment lead time must be less than the seasonal cycle in order to reduce the bullwhip effect. Therefore, the lead time needs to be reduced through collaboration between the retailer and supplier.     

A study on inventory replenishment policies in a two-echelon supply chain system

Inventory control plays an important role in supply chain management. Properly controlled inventory can satisfy customers’ demands, smooth the production plans, and reduce the operation costs; yet failing to budget the inventory expenses may lead to serious consequences. The bullwhip effect, observed in many supply chain management cases, causes excessive inventory due to information distortion, i.e. the order amount is exaggerated while a minor demand variation occurs, and the information amplified dramatically as the supply chain moves to the upstream. In this paper, one of the main causes of bullwhip effect, order batching, is considered. A simplified two-echelon supply chain system, with one supplier and one retailer that can choose different replenishment policies, is used as a demonstration. Two types of inventory replenishment methods are considered: the traditional methods (the event-triggered and the time-triggered ordering policies), and the statistical process control (SPC) based replenishment method. The results show that the latter outperforms the traditional method in the categories of inventory variation, and in the number of backlog when the fill-rate of the prior model is set to be 99%. This research provides a different approach to inventory cost-down other than the common methods like: information sharing, order batch cutting, and lead time reduction. By choosing a suitable replenishment policy, the number of backorder and the cost of inventory can be reduced.     

闭环供应链混合切换库存控制模型研究

针对一类具有回收、再制造、再分销的闭环供应链系统,以再制造产品的补货能力为切换信号设计了基于再制造优先的混合切换库存控制策略,使得市场需求优先由再制造产品满足,并应用切换控制理论研究混合切换库存控制策略的性能特征,分析系统参数对闭环供应链系统的关键性能指标的影响。仿真分析表明,合理的切换控制策略可以有效抑制闭环供应链运作过程的波动,保证系统具有良好的“牛鞭效应”特征、平稳的库存管理成本以及较高的顾客服务水平。     

自适应控制对多级库存延迟问题的优化研究

针对在随机需求下交货延迟所导致供应链多级库存系统库存积压、缺货和牛鞭效应等问题,建立了基于自适应控制算法的多级库存动态优化模型。通过泰勒展开和拉布拉斯变换建立了基于APIOBPCS策略考虑延迟的动态多级库存控制模型;由Lyapunov渐进稳定性定理设计了一种适用于多级库存的模型参考自适应控制算法,其中以无交货延迟的参考库存模型作为目标,通过调节线性补偿函数和自适应控制率,逐渐缩小实际库存模型与参考库存模型间的输出误差,以此削弱交货延迟对多级库存模型的影响;通过实证数据验证了模型参考自适应控制对一个三级供应链库存系统的动态优化效果。仿真结果表明,自适应控制下的无信息共享多级APIOBPCS库存系统缺货全部归零,牛鞭效应下降40.7%。在不增加企业运营投入的前提下,通过自适应控制算法,优化资源配置,动态削弱了交货延迟对多级库存的影响,提升了供应链运营效率。     

供应链存储系统无线射频识别使能的定量在制品法控制策略仿真

无线射频识别(radio frequency identification,RFID)技术的出现为库存控制策略的创新提供了一条有效的途径.本文利用RFID技术,将原有单个制造系统的流通卡系统推广到供应链的多级库存网络中,设计了RFID使能的电子流通卡系统.基于电子流通卡,实现了RFID使能的定量在制品法(constant work-in-process,CONWIP)控制策略;并建立了CONWIP控制策略的分销网络模型.为比较和验证CONWIP控制策略性能,开发了三级分销网络仿真系统,使用该系统,将其与RFID使能的(r,Q)策略进行比较,验证了CONWIP策略在一定条件下,能够有效降低存储成本、提高服务水平.     

滞后效应影响下低碳供应链减排投入与零售定价

考虑减排投资效果滞后效应的影响,构建低碳供应链纵向合作减排微分博弈模型.运用微分对策理论,得到分散式决策和集中式决策下低碳供应链的最优减排努力投入、宣传努力投入和零售定价策略,以及分散式决策下制造商的合作减排支付比例,并对不同决策机制下供应链成员的均衡策略进行比较分析.研究发现:集中式决策下,制造商减排努力投入和零售商宣传努力投入均高于分散式决策下的相应值;滞后时间存在一个阈值,只有滞后时间低于该阈值时,集中式决策才能提升整个供应链系统的经济绩效.     

电商平台主导下的供应链推广策略研究

结合电商平台快速发展的时代背景,构建了电商平台主导、制造商跟随的两级电商供应链博弈模型,分别研究了集中决策与分散决策下的产品定价、服务水平和推广水平,分析了佣金率对最优决策和供应链成员利润的影响,并设计了"推广成本分摊"策略.结果表明:当佣金率较低时,集中决策下的产品定价和服务水平、推广水平高于分散决策下的最优决策;当...     

PI补充策略下供应链牛鞭效应的$H_infty$控制

牛鞭效应是指供应链管理订单制定环节中因信息扭曲造成的需求逐级放大的一种现象.针对供应链中的节点企业,在订货点法的基础上加以改进构建新的订单制定规则,并构建$H_\infty$控制器达到抑制牛鞭效应的目的,从而降低供应链整体成本.订单制定环节由企业订单规则和需求预测两个部分组成,为应对需求持续上升使安全库存发散的情况,在订货点法的基础上设计PI补充策略下的新订单规则,并以系统$H_\infty$范数与供应链牛鞭效应的指标定义相同为基础,引入$H_\infty$控制器代替预测函数.仿真结果表明,所设计的PI 补充策略下的$H_\infty$控制器法与传统订单制定算法相比,可有效削减牛鞭效应,并且使企业库存始终维持在一个安全稳定的状态.     

Supply Chain Management by H-Infinity Control

In this paper, a H _infin control technique is proposed for the management of a supply chain (SC) model linearized about nominal operating conditions. The performance considered is a weighted H _infin norm comprising the inventory and the orders placed by each site, hence controlling the bullwhip effect together with local management costs. It is shown how the optimization of local costs at each site is related to the performance of the whole chain and a decentralized control methodology is proposed based on this relation.